What is expand (x-h)^4 ?

The solution to expand (x-h)^4 is x^4-4x^3h+6x^2h^2-4xh^3+h^4

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expand (x-h)^4

expand

(x - h)^{4}

x^{4} - 4 x^{3} h + 6 x^{2} h^{2} - 4 x h^{3} + h^{4}

Solution steps

(x - h)^{4}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = x, b = - h

= i = 0 \sum 4 (i 4) x^{(4 - i)} (- h)^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} (- h)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} (- h)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} (- h)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} (- h)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} (- h)^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} (- h)^{0} : x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} (- h)^{1} : - 4 x^{3} h

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} (- h)^{2} : 6 x^{2} h^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} (- h)^{3} : - 4 x h^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} (- h)^{4} : h^{4}

= x^{4} - 4 x^{3} h + 6 x^{2} h^{2} - 4 x h^{3} + h^{4}

\frac{i - 6}{3}

5^{- 3} \cdot 5

5 (a + b) + 2 (a + c) - 4 (b + c)

3 x^{3} + 9 x^{2} - 12 x

\frac{6}{7} + \frac{2}{5}

What is expand (x-h)^4 ?
The solution to expand (x-h)^4 is x^4-4x^3h+6x^2h^2-4xh^3+h^4